Speaker: Heejong Lee, University of Toronto

When: April 14, 2021 (Wed), 16:00--18:00.
Where: Building 110, Room N103.

Title: Serre weights of symplectic Galois representations

Abstract: In the late 20th century, there had been many studies on the connection between modular forms and Galois representation, highlighted by the proof of Taniyama-Shimura conjecture by Taylor and Wiles. This is now a part of Langlands program, whose goal is relating various L-functions in automorphic and arithmetic context.

One can also ask how the structure of one side is reflected on the other side. Serre conjectured that certain 2-dimensional mod p Galois representations arise from modular forms and specified the explicit weight and level of modular form that gives rise to a given mod p Galois representation. Higher dimensional analogue of the weight part of Serre's conjectures is formulated by Herzig and is proven by Le-Le Hung-Levin-Morra in their recent work.

In this talk, I will discuss the weight part of Serre's conjectures in higher dimension and how it is related to the representation of finite groups and lifting local Galois representations. Then I will explain the connection between these objects under the Langlands philosophy, to formulate the explicit Serre weight conjectures. If time permits, I will discuss the conjecture for the group GSp(4) and its relation to the case of GL(4).